American priest to make speech better (10)
I believe the answer is:
ameliorate
'better' is the definition.
('ameliorate' can be a synonym of 'better')
'american priest to make speech' is the wordplay.
'american' becomes 'am' (abbreviation in some contexts).
'priest' becomes 'eli' (I've seen this before).
'to make speech' becomes 'orate' (I've seen this in other clues).
'am'+'eli'+'orate'='AMELIORATE'
(Other definitions for ameliorate that I've seen before include "Make (a bad thing) better" , "Make (something) better" , "Become better" , "seen to improve" .)